In random edge pruning method, for each student hidden node, an incoming edge is kept with probability \(c = \raisebox {0.5ex}{\scalebox {0.8}{\displaystyle \lim _{N \rightarrow \infty }\;}}\frac{k_e}{N}\) . Majority of empirical studies throughout literature use random edge or node pruning as a baseline for empirical comparison (see papers in [1]}) making it an obvious candidate for our theoretical comparisons as well. It has been shown empirically by [2]} and theoretically by us that DPP node pruning is an above baseline node pruning method. In this section we show that baseline random edge pruning outperforms DPP node pruning which is consistent with the empirical observations that sparse models outperform dense models (section 3.2 of [1]}). Specifically, here we show that GE after random edge pruning is less than GE after DPP node pruning. Our proof proceeds as follows: (1) Theorem REF  gives a closed form expression for the GE after random edge pruning (2) Theorem REF  then shows that GE of random edge pruning is less than GE of DPP node pruning.
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